Related papers: Hitting times of threshold exceedances and their d…
We present simulation results for the contact process on regular, cubic networks that are composed of a one-dimensional lattice and a set of long edges with unbounded length. Networks with different sets of long edges are considered, that…
Any limiting point process for the time normalized exceedances of high levels by a stationary sequence is necessarily compound Poisson under appropriate long range dependence conditions. Typically exceedances appear in clusters. The…
In this paper, we investigate random walks in a family of small-world trees having an exponential degree distribution. First, we address a trapping problem, that is, a particular case of random walks with an immobile trap located at the…
Many biological, social, and communication systems can be modeled by ``searchers'' moving through a complex network. For example, intracellular cargo is transported on tubular networks, news and rumors spread through online social networks,…
Here tree dependency structures are studied from three different perspectives: their degree variance (hubiness), the mean dependency length and the number of dependency crossings. Bounds that reveal pairwise dependencies among these three…
Numerous systems ranging from deformation of materials to earthquakes exhibit bursty dynamics, which consist of a sequence of events with a broad event size distribution. Very often these events are observed to be temporally correlated or…
Two node variables determine the evolution of cascades in random networks: a node's degree and threshold. Correlations between both fundamentally change the robustness of a network, yet, they are disregarded in standard analytic methods as…
External or internal shocks may lead to the collapse of a system consisting of many agents. If the shock hits only one agent initially and causes it to fail, this can induce a cascade of failures among neighoring agents. Several critical…
Networks of person-person contacts form the substrate along which infectious diseases spread. Most network-based studies of the spread focus on the impact of variations in degree (the number of contacts an individual has). However, other…
The asymptotics of the probability that the self-intersection local time of a random walk on $\Z^d$ exceeds its expectation by a large amount is a fascinating subject because of its relation to some models from Statistical Mechanics, to…
Several systems can be modeled as sets of interdependent networks where each network contains distinct nodes. Diffusion processes like the spreading of a disease or the propagation of information constitute fundamental phenomena occurring…
Online social networks have increasing influence on our society, they may play decisive roles in politics and can be crucial for the fate of companies. Such services compete with each other and some may even break down rapidly. Using social…
Motivated by the analysis of social networks, we study a model of random networks that has both a given degree distribution and a tunable clustering coefficient. We consider two types of growth processes on these graphs: diffusion and…
Threshold models of global cascades have been extensively used to model real-world collective behavior, such as the contagious spread of fads and the adoption of new technologies. A common property of those cascade models is that a…
A fundamental property of complex networks is the tendency for edges to cluster. The extent of the clustering is typically quantified by the clustering coefficient, which is the probability that a length-2 path is closed, i.e., induces a…
We introduce a new threshold model of social networks, in which the nodes influenced by their neighbours can adopt one out of several alternatives. We characterize social networks for which adoption of a product by the whole network is…
Random links between otherwise distant nodes can greatly facilitate the propagation of disease or information, provided contagion can be transmitted by a single active node. However we show that when the propagation requires simultaneous…
The epidemic threshold of a spreading process indicates the condition for the occurrence of the wide spreading regime, thus representing a predictor of the network vulnerability to the epidemic. Such threshold depends on the natural history…
Current understanding of the critical outbreak condition on temporal networks relies on approximations (time scale separation, discretization) that may bias the results. We propose a theoretical framework to compute the epidemic threshold…
Hysteresis loops and the associated avalanche statistics of spin systems, such as the random-field Ising and Edwards-Anderson spin-glass models, have been extensively studied. A particular focus has been on self-organized criticality,…